Several come from here: https://venngage.com/blog/bad-infographics/

• We provide some general principles we can use as a guide for effective data visualization.

• Much of this section is based on a talk by Karl Broman¹ titled “Creating Effective Figures and Tables”² and includes some of the figures which were made with code that Karl makes available on his GitHub repository³, as well as class notes from Peter Aldhous’ Introduction to Data Visualization course⁴.

• Following Karl’s approach, we show some examples of plot styles we should avoid, explain how to improve them, and use these as motivation for a list of principles.

• We compare and contrast plots that follow these principles to those that don’t.

• The principles are mostly based on research related to how humans detect patterns and make visual comparisons.

• The preferred approaches are those that best fit the way our brains process visual information.

• When deciding on a visualization approach, it is also important to keep our goal in mind.

We may be comparing a

• viewable number of quantities
• describing distributions for categories or numeric values
• comparing the data from two groups
• or describing the relationship between two variables.

We start by describing some principles for encoding data. There are several approaches at our disposal including:

• aligned lengths
• position
• angles
• area
• brightness
• color hue.

• Suppose we want to report the results from two hypothetical polls regarding browser preference taken in 2000 and then 2015.

• For each year, we are simply comparing five quantities – the five percentages.

• A widely used graphical representation of percentages, popularized by Microsoft Excel, is the pie chart:

• Here we are representing quantities with both areas and angles, since both the angle and area of each pie slice are proportional to the quantity the slice represents.

• This turns out to be a sub-optimal choice since, as demonstrated by perception studies, humans are not good at precisely quantifying angles and are even worse when area is the only available visual cue.

The donut chart is an example of a plot that uses only area:

• Can you determine the actual percentages and rank the browsers’ popularity?

• Can you see how the percentages changed from 2000 to 2015?

A better approach is to simply show the numbers. It is not only clearer, but would also save on printing costs if printing a paper copy:

#> Warning in !is.null(rmarkdown::metadata$output) && rmarkdown::metadata$output
#> %in% : 'length(x) = 3 > 1' in coercion to 'logical(1)'

Because length is the best visual cue, barplots provide the best visualization for a series of proportions:

Label each pie slice with its respective percentage so viewers do not have to infer them from the angles or area:

• When using barplots, it is misinformative not to start the bars at 0.

• This is because, by using a barplot, we are implying the length is proportional to the quantities being displayed.

• By avoiding 0, relatively small differences can be made to look much bigger than they actually are.

• This approach is often used by politicians or media organizations trying to exaggerate a difference.

Below is an illustrative example used by Peter Aldhous in this lecture: http://paldhous.github.io/ucb/2016/dataviz/week2.html.

(Source: Fox News, via Media Matters⁵.)

(Source: Fox News, via Flowing Data⁶.)

(Source: Venezolana de Televisión via Pakistan Today⁷ and Diego Mariano.)

Here is the appropriate plot:

• When using position rather than length, it is then not necessary to include 0.

• This is particularly the case when we want to compare differences between groups relative to the within-group variability.

During President Barack Obama’s 2011 State of the Union Address, the following chart was used to compare the US GDP to the GDP of four competing nations:

(Source: The 2011 State of the Union Address⁸)

Here is comparison of using radius versus arae:

Not surprisingly, ggplot2 defaults to using area rather than radius.

Of course, in this case, we really should not be using area at all since we can use position and length:

• When one of the axes is used to show categories the default ggplot2 behavior is to order the categories alphabetically when they are defined by character strings.

• If they are defined by factors, they are ordered by the factor levels.

• We rarely want to use alphabetical order.

• Instead, we should order by a meaningful quantity.

Note tjat the plot on the right is more informative:

We can make the second plot like this:

data(murders)
murders |> mutate(murder_rate = total / population * 100000) |>
  mutate(state = reorder(state, murder_rate)) |>
  ggplot(aes(state, murder_rate)) +
  geom_bar(stat="identity") +
  coord_flip() +
  theme(axis.text.y = element_text(size = 6)) +
  xlab("")

Here is another example:

We have focused on displaying single quantities across categories. We now shift our attention to displaying data, with a focus on comparing groups.

Supppose we want to describe the heigh data to an extra-terrestrial.

A commonly used plot, popularized by Microsoft Excel, is a barplot like this:

heights |> 
  ggplot(aes(sex, height)) + 
  geom_point() 

But this plot can be improved as there is much over-plotting

THis is achieved using jitter:

heights |> 
  ggplot(aes(sex, height)) +
  geom_jitter(width = 0.1, alpha = 0.2) 

Since there are so many points, it is more effective to show distributions rather than individual points. We therefore show histograms for each group:

• Use common axes

• If horizontal comparison, stack graphs vertically

• If vertical comparison, stack graphs horizontally

heights |> 
  ggplot(aes(height, ..density..)) +
  geom_histogram(binwidth = 1, color="black") +
  facet_grid(sex~.)

Stack horizontally

 heights |> 
  ggplot(aes(sex, height)) + 
  geom_boxplot(coef=3) + 
  geom_jitter(width = 0.1, alpha = 0.2) +
  ylab("Height in inches")

Here is a terribly plot comparing population across continents

Using a log transformation here provides a much more informative plot. Compare these two plots:

• logit

• sqrt

Note that it is hard to compare 1970 to 2020 by country:

Much easier if they are adjacent

The comparison becomes even easier to make if we use color to denote the two things we want to compare:

 gapminder |> 
  filter(year %in% c(1970, 2010) & !is.na(gdp)) |>
  mutate(dollars_per_day = gdp/population/365, year = factor(year)) |>
  ggplot(aes(continent, dollars_per_day, fill = year)) +
  geom_boxplot() + 
  theme(axis.text.x = element_text(angle = 90, hjust = 1)) +
  scale_y_continuous(trans = "log2") + 
  ylab("Income in dollars per day")

An example of how we can use a color blind friendly palette is described here: http://www.cookbook-r.com/Graphs/Colors_(ggplot2)/#a-colorblind-friendly-palette:

color_blind_friendly_cols <- 
  c("#999999", "#E69F00", "#56B4E9", "#009E73", 
    "#F0E442", "#0072B2", "#D55E00", "#CC79A7")

Here are the colors

There are several resources that can help you select colors, for example this one: http://bconnelly.net/2013/10/creating-colorblind-friendly-figures/.

In general, you should use scatterplots to visualize the relationship between two variables.

However, there are some exceptions and we describe two alternative plots here: the slope chart and the Bland-Altman plot.

Slope charts adds angle as a visual cue, useful when comparing two groups and each element across two variables, such as years.

west <- c("Western Europe","Northern Europe","Southern Europe",
          "Northern America","Australia and New Zealand")

dat <- gapminder |> 
  filter(year%in% c(2010, 2015) & region %in% west & 
           !is.na(life_expectancy) & population > 10^7) 

dat |>
  mutate(location = ifelse(year == 2010, 1, 2), 
         location = ifelse(year == 2015 & 
                             country %in% c("United Kingdom", "Portugal"),
                           location+0.22, location),
         hjust = ifelse(year == 2010, 1, 0)) |>
  mutate(year = as.factor(year)) |>
  ggplot(aes(year, life_expectancy, group = country)) +
  geom_line(aes(color = country), show.legend = FALSE) +
  geom_text(aes(x = location, label = country, hjust = hjust), 
            show.legend = FALSE) +
  xlab("") + ylab("Life Expectancy")

library(ggrepel)
dat |> 
  mutate(year = paste0("life_expectancy_", year)) |>
  select(country, year, life_expectancy) |> 
  pivot_wider(names_from = "year", values_from="life_expectancy") |> 
  mutate(average = (life_expectancy_2015 + life_expectancy_2010)/2,
         difference = life_expectancy_2015 - life_expectancy_2010) |>
  ggplot(aes(average, difference, label = country)) + 
  geom_point() +
  geom_text_repel() +
  geom_abline(lty = 2) +
  xlab("Average of 2010 and 2015") + 
  ylab("Difference between 2015 and 2010")

We can use

• different colors or shapes for categoris

• areas, brightness or hue for continuous values

Below is an example that encodes three variables: OPEC membership, region, and population.

When selecting colors to quantify a numeric variable, we choose between two options: sequential and diverging.

Sequential colors are suited for data that goes from high to low. High values are clearly distinguished from low values. Here are some examples offered by the package RColorBrewer:

library(RColorBrewer)
display.brewer.all(type="seq")

Diverging colors are used to represent values that diverge from a center. We put equal emphasis on both ends of the data range: higher than the center and lower than the center.

library(RColorBrewer)
display.brewer.all(type="div")

The figure below, taken from the scientific literature⁹, shows three variables: dose, drug type and survival.

(Image courtesy of Karl Broman)

Humans are not good at seeing in three dimensions and our limitation is even worse with regard to pseudo-three-dimensions.

Try to determine the values of the survival variable in the previous plot.

Can you tell when the purple ribbon intersects the red one?

This is an example in which we can easily use color to represent the categorical variable instead of using a pseudo-3D:

Pseudo-3D is sometimes used completely gratuitously: plots are made to look 3D even when the 3rd dimension does not represent a quantity. This only adds confusion and makes it harder to relay your message. We show two examples:

(Images courtesy of Karl Broman)

• By default, statistical software like R returns many significant digits.

• The default behavior in R is to show 7 significant digits.

• That many digits often adds no information and the added visual clutter can make it hard for the viewer to understand the message.

As an example, here are the per 10,000 disease rates, computed from totals and population in R, for California across the five decades:

• We are reporting precision up to 0.00001 cases per 10,000, a very small value in the context of the changes that are occurring across the dates.

• In this case, two significant figures is more than enough and clearly makes the point that rates are decreasing:

Useful ways to change the number of significant digits or to round numbers are

• signif

• round

You can define the number of significant digits globally by setting options like this: options(digits = 3).

Another principle related to displaying tables is to place values being compared on columns rather than rows. Compare these two presentations:

Graphs can be used for

1. our own exploratory data analysis,

2. to convey a message to experts, or

3. to help tell a story to a general audience.

Make sure that the intended audience understands each element of the plot.